The invention relates generally to signal processing. In particular, the invention relates to error reduction during roll/pitch/yaw coordinate transformation using covariance matrices.
Modern combat systems comprise an ever-increasing number and diversity of sensors. The function of a sensor is to provide information, typically in the form of numerical values, of the quantity that sensor is designed to detect and measure. In spite of the wide types and diversities of the sensors in a modern combat system, they all possess one very important property in common, namely that they all report out measurement data that contains errors. These errors, while undesirable, are unavoidable due to many reasons, among which are the following two:
(a) Finite resolution of the measurement electronics.
(b) Impact of ambient temperature and humidity on the electronics.
The type of errors being referred to here are commonly referred to as “noise”, meaning that the errors very randomly from one measurement to another. In one measurement, the value reported is slightly higher (positive error) than the true value and in the next, slightly lower (negative). Over the long term, the average error is zero, meaning that the sum of the positive and negative errors typically averages out to zero.
The particular sensor involved in providing exemplary embodiments operates with a component of every inertial navigation system on board every navigable vessel on the sea, in the air and also in space. This component is commonly known as the roll/pitch/yaw (r, p, w) angle measurement system. This system plays a critical role in all combat systems, including those that operate a radar transceiver. Consider a radar on board a combat ship. The sea represents an unstable environment because the ocean waves and currents cause the ship to toss about—i.e., to rotate about at least one of the ship's axes: longitudinal (stern-to-bow), lateral (starboard-to-port) and vertical (keel-to-deck).
Translations in the longitudinal, lateral and vertical axes are respectively called surge, sway and heave. Rotations about the longitudinal, lateral and vertical axes are respectively called roll, pitch and yaw. This motion can be quite severe under sufficiently high sea states. A radar on board that ship is also subject to the same rolling, pitching and yawing motion.